用tensorflow构建神经网络学习简单函数

目标是学习\(y=2x+3\)

建立一个5层的神经网络，用平方误差作为损失函数。

代码如下：

import tensorflow as tf
import numpy as np
import time

x_size=200000
dim=2
x_data=np.random.random([x_size,dim]).astype('float32')
y_data=2*x_data+3
x_test=np.random.random([10,dim]).astype('float32')
y_test=2*x_test+3

train_x=tf.placeholder(tf.float32,shape=[None,dim])
train_y=tf.placeholder(tf.float32,shape=[None,dim]) 

weight1=tf.Variable(tf.truncated_normal([dim,40],stddev=0.1))
b1=tf.Variable(tf.zeros([40])+0.1)
h1=tf.nn.relu(tf.matmul(train_x,weight1)+b1)

weight2=tf.Variable(tf.truncated_normal([40,40],stddev=0.1))
b2=tf.Variable(tf.zeros([40])+0.1)
h2=tf.nn.relu(tf.matmul(h1,weight2)+b2)

weight3=tf.Variable(tf.truncated_normal([40,40],stddev=0.1))
b3=tf.Variable(tf.zeros([40])+0.1)
h3=tf.nn.relu(tf.matmul(h2,weight3)+b3)

weight4=tf.Variable(tf.truncated_normal([40,40],stddev=0.1))
b4=tf.Variable(tf.zeros([40])+0.1)
h4=tf.nn.relu(tf.matmul(h3,weight4)+b4)

weight5=tf.Variable(tf.truncated_normal([40,dim],stddev=0.1))
b5=tf.Variable(tf.zeros([dim])+0.1)
y_output=tf.nn.relu(tf.matmul(h4,weight5)+b5)

loss=tf.reduce_mean(tf.square(train_y-y_output))
optimizer=tf.train.GradientDescentOptimizer(0.5)
train_step=optimizer.minimize(loss)

t1=time.time()
sess=tf.Session()
sess.run(tf.global_variables_initializer())
for i in range(2000):
    feed_train={
        train_x:x_data,
        train_y:y_data
    }
    if i%100==0:
        print('loss:',sess.run(loss,feed_dict=feed_train),end=',   ')
    sess.run(train_step,feed_dict=feed_train)
print()
t2=time.time()
print('Total Time:',t2-t1)
print('test')
for i in range(10):
    feed_test={train_x:x_test[i:i+1],train_y:y_test[i:i+1]}
    print('y:       ',sess.run(train_y,feed_dict=feed_test))
    print('y_output:',sess.run(y_output,feed_dict=feed_test))
    print('loss:',sess.run(loss,feed_dict=feed_test))
sess.close()

结果：

loss: 15.4106,   loss: 0.232037,   loss: 0.211914,   loss: 0.198133,   loss: 0.0544874,   loss: 0.0280089,   loss: 0.0211618,   loss: 0.0173591,   loss: 0.0109964,   loss: 0.00902615,   loss: 0.00815686,   loss: 0.00941989,   loss: 0.00619169,   loss: 0.00529554,   loss: 0.00506653,   loss: 0.00660528,   loss: 0.00382864,   loss: 0.00412649,   loss: 0.00610038,   loss: 0.00354737,
Total Time: 88.89598035812378
test
y:        [[ 4.46494102  4.53034449]]
y_output: [[ 4.48269606  4.44468594]]
loss: 0.00382631
y:        [[ 3.21122026  4.36406898]]
y_output: [[ 3.22117805  4.2706871 ]]
loss: 0.00440967
y:        [[ 3.58840036  4.41665506]]
y_output: [[ 3.59200501  4.3375597 ]]
loss: 0.00313453
y:        [[ 3.49797821  4.21883869]]
y_output: [[ 3.51356149  4.14429617]]
loss: 0.00289971
y:        [[ 3.75655651  4.35610151]]
y_output: [[ 3.76163697  4.26597834]]
loss: 0.004074
y:        [[ 4.52173853  4.32090807]]
y_output: [[ 4.53192806  4.2343545 ]]
loss: 0.00379767
y:        [[ 4.19067335  4.8417387 ]]
y_output: [[ 4.20001888  4.73385048]]
loss: 0.0058636
y:        [[ 4.58287668  3.89965653]]
y_output: [[ 4.59979439  3.84099913]]
loss: 0.00186345
y:        [[ 4.25389147  3.75640154]]
y_output: [[ 4.23791742  3.69044876]]
loss: 0.00230247
y:        [[ 3.40870714  4.49888897]]
y_output: [[ 3.41926885  4.42829704]]
loss: 0.00254738

可以看出在训练集上loss不断减小，最后下降到0.00354737，而在测试集上loss也在0.003左右。

由于参数是随机设置的，有时候可能陷入局部最优中，多运行几次可以减少陷入局部最优的概率。

将优化算法换成：

optimizer=tf.train.AdamOptimizer()

后的结果：

loss: 15.6427,   loss: 0.197051,   loss: 0.174776,   loss: 0.164641,   loss: 0.15766,   loss: 0.131154,   loss: 0.0029341,   loss: 0.000404288,   loss: 0.000178629,   loss: 9.63827e-05,   loss: 5.74653e-05,   loss: 3.65505e-05,   loss: 2.44332e-05,   loss: 1.69916e-05,   loss: 1.22397e-05,   loss: 9.06447e-06,   loss: 6.86902e-06,   loss: 5.31113e-06,   loss: 4.16228e-06,   loss: 3.30907e-06,
Total Time: 89.90041589736938
test
y:        [[ 4.46494102  4.53034449]]
y_output: [[ 4.46485758  4.53046322]]
loss: 1.05304e-08
y:        [[ 3.21122026  4.36406898]]
y_output: [[ 3.21072125  4.36450434]]
loss: 2.19271e-07
y:        [[ 3.58840036  4.41665506]]
y_output: [[ 3.58802533  4.41699553]]
loss: 1.28282e-07
y:        [[ 3.49797821  4.21883869]]
y_output: [[ 3.49763799  4.2191186 ]]
loss: 9.70489e-08
y:        [[ 3.75655651  4.35610151]]
y_output: [[ 3.75626636  4.35636234]]
loss: 7.61112e-08
y:        [[ 4.52173853  4.32090807]]
y_output: [[ 4.52174997  4.32091379]]
loss: 8.18545e-11
y:        [[ 4.19067335  4.8417387 ]]
y_output: [[ 4.19037819  4.84208441]]
loss: 1.03317e-07
y:        [[ 4.58287668  3.89965653]]
y_output: [[ 4.58305788  3.89945245]]
loss: 3.7242e-08
y:        [[ 4.25389147  3.75640154]]
y_output: [[ 4.25399828  3.75623488]]
loss: 1.95912e-08
y:        [[ 3.40870714  4.49888897]]
y_output: [[ 3.40823555  4.49932337]]
loss: 2.05551e-07

使用RMSPropOptimizer，最小loss:0.33
使用FtrlOptimizer，最小loss:0.17
使用MomentumOptimizer(learning_rate=0.1,momentum=0.6)，loss:4.47119e-06， 但是不是很稳定。